A173114 a(0)=a(1)=1, a(n) = 2*a(n-1)- A010686(n), n>1.

1, 1, 1, -3, -7, -19, -39, -83, -167, -339, -679, -1363, -2727, -5459, -10919, -21843, -43687, -87379, -174759, -349523, -699047, -1398099, -2796199, -5592403, -11184807, -22369619, -44739239, -89478483, -178956967, -357913939, -715827879, -1431655763

Offset: 0

Author

Paul Curtz, Feb 10 2010

Keywords

• easy
• sign

Comments

The sequence in the first row and successive differences in followup rows defines the array

1, 1, 1, -3, -7, -19, -39, -83, -167, -339, ..

0, 0, -4, -4, -12, -20, -44, -84, -172, -340, ..

0, -4, 0, -8, -8, -24, -40, -88, -168, -344, ..

-4, 4, -8, 0, -16, -16, -48, -80, -176, -336, ..

8, -12, 8, -16, 0, -32, -32, -96, -160, -352, ..

The first two subdiagonals show essentially the powers of 2.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Formula

a(n) = 3 + 2*( (-1)^n-2^n )/3 = 3-A078008(n+1), n>0. - R. J. Mathar, Jun 30 2010

a(n+2)-a(n)= A154589(n+2) = -2^(n+1), n>0.

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3), n>3.

G.f.: (-x-2*x^2-4*x^3+1)/( (1-x)*(1-2*x)*(1+x) ).

a(n) + A173078(n) = 2^n.

a(n) - a(n-1) = -4*A001045(n-2) = -A097074(n-1), n>1.

Extensions

Edited and extended by R. J. Mathar, Jun 30 2010